Abstract:

The basis for this study rests upon the question whether typical human reasoning is reliant upon the application of formal inference rules or not. Two major approaches on this topic, formal logic and mental model theory, are considered. The purpose of the literature review is to provide the reader with an overview of the principles and preliminary concepts of formal logic and mental model theory on reasoning. A particular area of human reasoning that is of interest is default reasoning and its relation to beliefs and belief revision. Fallacious deductive reasoning and biases in human reasoning are thoroughly discussed; and we propose possible ordinary language nuances (specifically, human reasoner interpretation of 'only if statements).
An investigation into specific observations and hypotheses — mentioned in the latter
discussions on the idiosyncrasies of human reasoning — is conducted with a small sample of undergraduate students of Rand Afrikaans University (with some preliminary training in formal logic), registered for and satisfying the requirements necessary to study either the Mathematics 1 or the Mathematics 3 course offered by the university for the academic year 2002. Survey findings articulate correspondence between all survey participants and reasoners without any formal training in mathematical logic (in previous studies of human reasoning referred to in literature) in terms of performance on modus tollens as opposed to modus ponens problems, and the rate at which affirming the consequent and denying the antecedent occur. Of further interest are survey results on questions testing responses to alternative format modus ponens and modus tollens inferences, and inferences affirming the consequent and denying the antecedent;
fallacious inferences made from specific standard form categorical propositions; whether or not the formal logical interpretation of 'only if' statements is made; and participant tendency to engage in default reasoning.